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Evaluate the Integral by Making a Substitution and Then Using cosθsinθ49+sin2θdθ\int \frac { \cos \theta } { \sin \theta \sqrt { 49 + \sin ^ { 2 } \theta } } d \theta

Question 265

Multiple Choice

Evaluate the integral by making a substitution and then using a table of integrals.
- cosθsinθ49+sin2θdθ\int \frac { \cos \theta } { \sin \theta \sqrt { 49 + \sin ^ { 2 } \theta } } d \theta


A) 17ln7+49+sin2θsinθ+C- \frac { 1 } { 7 } \ln \left| \frac { 7 + \sqrt { 49 + \sin ^ { 2 } \theta } } { \sin \theta } \right| + C
B) 17ln7cosθ+49+sin2θsinθ+C- \frac { 1 } { 7 } \ln \left| \frac { 7 \cos \theta + \sqrt { 49 + \sin ^ { 2 } \theta } } { \sin \theta } \right| + C
C) 17ln749+sin2θsinθ+C- \frac { 1 } { 7 } \ln \left| \frac { 7 - \sqrt { 49 + \sin ^ { 2 } \theta } } { \sin \theta } \right| + C
D) 17ln7+49+sin2θsinθcosθ+C- \frac { 1 } { 7 } \ln \left| \frac { 7 + \sqrt { 49 + \sin ^ { 2 } \theta } } { \sin \theta \cos \theta } \right| + C

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